May/June 2026 Paper 13

2026 · 11 questions · 23 parts · 75 marks

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11(a)11(b)11(c)

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8Areas Volumes Arc LengthHard5 marks

Graph of the curve $y=\dfrac{2}{5x^{3}}$, a decreasing curve for $x>0$ that falls steeply near the $y$-axis and flattens as $x$ increases; the shaded region is bounded above by the curve, below by the $x$-axis, and on the sides by the vertical lines $x=1$ and $x=t$ (with $t>1$), shown as the shaded strip between those two lines.

The diagram shows part of the curve with equation

y = \frac{2}{5 x ^{3}}

.

The shaded region is bounded by the curve, the

x

-axis and the lines

x = 1

and

x = t

. It is given that the area of the shaded region is

\frac{1}{9}

.

Find the value of

t

.

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